Solve the system of equations.

Question

9x + y = 2
–4x – y = –17

I don't understand how you solve this.

Answer 1

Add the two equations to cancel out y.

5x = -15

You should be able to work it from there.

Answer 2

9 x + y = 2 Subtract 9 x to both sides

9 x + y - 9 x = 2 - 9 x

y = 2 - 9 x

–4 x – y = – 17

–4 x – ( 2 - 9 x ) = – 17

- 4 x - 2 - ( - 9 x ) = - 17

- 4 x - 2 + 9 x = - 17

- 4 x + 9 x - 2 = - 17

5 x - 2 = - 17 Add 2 to both sides

5 x - 2 + 2 = - 17 + 2

5 x = - 15 Divide both sides by 5

5 x / 5 = - 15 / 5

x = - 3

y = 2 - 9 x = 2 - 9 * ( - 3 ) = 2 + 9 * 3 = 2 + 27 = 29

The solution :

x = - 3 , y = 29

Proof :

9 x + y = 2

9 * ( - 3 ) + 29 = 2

- 27 + 29 = 2

2 = 2

– 4 x – y = – 17

- 4 * ( - 3 ) - 29 = - 17

4 * 3 - 29 = - 17

12 - 29 = - 17

- 17 = - 17